R Notebook

library(readr)
library(tidyverse)
library(scales)
library(plotly)
Full_centrality <- read_csv("Full_centrality.csv", 
    col_types = cols(X1 = col_skip(), 
                     page_id = col_character(), 
                     page_name = col_character(),
                     week = col_date(format = "%Y-%m-%d")))

library(readr)
page_name_map <- read_csv("page_name_map.csv", 
                          col_types = cols(
                            page_id = col_character(), 
                            page_name = col_character()
                          ))


Full_centrality = Full_centrality %>% left_join(page_name_map, by='page_id') %>% select(-X1) %>%relocate(page_name, .after = page_id) 

不同種類中心性

Degree Centrality

簡而言之就是總觸及率

week_1 = min(Full_centrality$week)

top10.deg.centrality.week1 = Full_centrality %>% filter(week == week_1) %>% arrange(desc(degree_centrality)) %>% select(page_name) %>% head(10) %>% pull


top10.deg.centrality.all = Full_centrality %>% filter(page_name %in% top10.deg.centrality.week1) %>% select(page_name,degree_centrality, week)


(top10.deg.centrality.all %>% ggplot() + 
  geom_line(aes(y = degree_centrality, x = week, color=page_name)) +
  scale_x_date(labels = date_format("%Y-%m"))) %>% ggplotly

Eigenvalue Centrality

與結點互動的對象中心性越高，自己的中心性就會越高

\[ C_E^{user} = \frac{1}{\lambda} \sum_{p \in page} C_E^{page}(p) a_{ip} \\ C_E^{page} = \frac{1}{\lambda} \sum_{u \in user} C_E^{user}(u) a_{iu} \]

top10.eig.centrality.week1 = Full_centrality %>% filter(week == week_1) %>% arrange(desc(eigenvector_centrality)) %>% select(page_name) %>% head(10) %>% pull


top10.eig.centrality.all = Full_centrality %>% filter(page_name %in% top10.eig.centrality.week1) %>% select(page_name,eigenvector_centrality, week)


top10.eig.centrality.all %>% ggplot() + 
  geom_line(aes(y = eigenvector_centrality, x = week, color=page_name)) +
  scale_x_date(labels = date_format("%Y-%m-%d"))

top10.unweighted.eig.centrality.week1 = Full_centrality %>% filter(week == week_1) %>% arrange(desc(unweighted_eigenvector_centrality)) %>% select(page_name) %>% head(10) %>% pull


top10.unweighted.eig.centrality.all = Full_centrality %>% filter(page_name %in% top10.unweighted.eig.centrality.week1) %>% select(page_name,unweighted_eigenvector_centrality, week)


top10.unweighted.eig.centrality.all %>% ggplot() + 
  geom_line(aes(y = unweighted_eigenvector_centrality, x = week, color=page_name)) +
  scale_x_date(labels = date_format("%Y-%m-%d"))

Narmalize 後容易被 outlire 影響（10月上下，有一個用戶特別勤奮對其中一個粉專按讚，則他與那個粉專的中心性都會增加）

Closeness Centrality

到其他節點的平均距離（次數）越高，中心性越小。

top10.cls.centrality.week1 = Full_centrality %>% filter(week == week_1) %>% arrange(desc(closeness_centrality)) %>% select(page_name) %>% head(10) %>% pull


top10.cls.centrality.all = Full_centrality %>% filter(page_name %in% top10.cls.centrality.week1) %>% select(page_name,closeness_centrality, week)


(top10.cls.centrality.all %>% ggplot() + 
  geom_line(aes(y = closeness_centrality, x = week, color=page_name)) +
  scale_x_date(labels = date_format("%Y-%m"))) %>% ggplotly

互動次數在計算過程中不具意義，較不具代表性的衡量

Current Flow Betweenness Centrality

如果以其中一個粉專/用戶作為消息來源起點(source)，另外一個粉專/用戶作為消息終點(sink)，則關注的節點對於資訊流量的貢獻有多少？

該節點在每一對節點之間的流量總和，就是Current flow betweenness centrality。

計算上模擬電流運作 https://tinyurl.com/27dcmgj5

What happned in 2016-09-25?

top10.unweighted.eig.centrality.week_other = Full_centrality %>% filter(week == '2016-09-25') %>% arrange(desc(unweighted_eigenvector_centrality)) %>% select(page_name) %>% head(3) %>% pull


top10.unweighted.eig.centrality.all = Full_centrality %>% filter(page_name %in% c(top10.unweighted.eig.centrality.week1[1:3], top10.unweighted.eig.centrality.week_other)) %>% select(page_name,unweighted_eigenvector_centrality, week)


p = top10.unweighted.eig.centrality.all %>% ggplot() + 
  geom_line(aes(y = unweighted_eigenvector_centrality, x = week, color=page_name)) +
  scale_x_date(labels = date_format("%Y-%m-%d"))

ggplotly(p)

top10.eig.centrality.week_other = Full_centrality %>% filter(week == '2016-10-02') %>% arrange(desc(eigenvector_centrality)) %>% select(page_name) %>% head(4) %>% pull


top10.eig.centrality.all = Full_centrality %>% filter(page_name %in% c(top10.eig.centrality.week1[1:4], top10.eig.centrality.week_other)) %>% select(page_name,unweighted_eigenvector_centrality, week)


p = top10.eig.centrality.all %>% ggplot() + 
  geom_line(aes(y = unweighted_eigenvector_centrality, x = week, color=page_name)) +
  scale_x_date(labels = date_format("%Y-%m-%d"))

ggplotly(p)

社群偵測 Community Detection

將用戶粉專互動的社會網路投影到只有粉專的社會網路上，並以此進行community detection（透過 Louvain algorithm），可以大致的偵測出支持川普陣營的粉專，以及希拉蕊陣營的粉專。

以下將各個陣營的粉專的各種中心性取平均，畫出隨時間的變化圖

library(readr)
avg_centrality_panel <- read_csv("avg_centrality_panel.csv", 
    col_types = cols(week = col_date(format = "%Y-%m-%d")))
avg_centrality_panel$community = factor(
                      avg_centrality_panel$community,
                      levels = c('Trump', 'Clinton','others'))

plot_avg_centrality = function(col_name, title_name){
  avg_centrality_panel %>% ggplot() +
  geom_line(aes(x = week, y = .data[[col_name]], color = community)) +
  scale_x_date(labels = date_format("%Y-%m-%d")) + 
  ggtitle(paste(title_name, "Change")) +
  ylab(title_name)
}

plot_avg_centrality('degree_centrality', 
                    'Degree Centrality')

plot_avg_centrality('eigenvector_centrality', 
                    'Eigenvector Centrality')

plot_avg_centrality('unweighted_eigenvector_centrality', 
                    'Unweighted Eigenvector Centrality')

plot_avg_centrality('closeness_centrality', 
                    'Closeness Centrality')